Advanced semi-analytical techniques for the q-fractional Ivancevic option pricing model
This study investigates the q-fractional Ivancevic option pricing model using two advanced semi-analytical methods: the q-Laplace Residual Power Series Method (q-LRPSM) and the q-Homotopy Analysis Method (q-HAM). The q-LRPSM is introduced and adapted for the first time to solve q-fractional partial...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-10-01
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| Series: | Ain Shams Engineering Journal |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2090447925003867 |
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| author | Khalid K. Ali Mohamed S. Mohamed M. Maneea |
| author_facet | Khalid K. Ali Mohamed S. Mohamed M. Maneea |
| author_sort | Khalid K. Ali |
| collection | DOAJ |
| description | This study investigates the q-fractional Ivancevic option pricing model using two advanced semi-analytical methods: the q-Laplace Residual Power Series Method (q-LRPSM) and the q-Homotopy Analysis Method (q-HAM). The q-LRPSM is introduced and adapted for the first time to solve q-fractional partial differential equations, offering accurate and efficient approximate solutions through a power series approach. The q-HAM builds on the traditional HAM by constructing a homotopy between an initial guess and the exact solution. Numerical simulations confirm the effectiveness and accuracy of both methods across various q-values and time steps, with 2D and 3D visualizations highlighting their rapid convergence. The study demonstrates that these methods provide a powerful framework for solving complex models in financial mathematics and applied sciences. |
| format | Article |
| id | doaj-art-42c19f576c274f0c89a2faabfdd89e82 |
| institution | Kabale University |
| issn | 2090-4479 |
| language | English |
| publishDate | 2025-10-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Ain Shams Engineering Journal |
| spelling | doaj-art-42c19f576c274f0c89a2faabfdd89e822025-08-20T03:58:41ZengElsevierAin Shams Engineering Journal2090-44792025-10-01161010364510.1016/j.asej.2025.103645Advanced semi-analytical techniques for the q-fractional Ivancevic option pricing modelKhalid K. Ali0Mohamed S. Mohamed1M. Maneea2Mathematics Department, Faculty of Science, Al-Azhar University, Nasr-City, Cairo, Egypt; Corresponding author.Department of Mathematics, College of Science, Taif University, P.O. Box 11099, Taif, 21944, Saudi ArabiaFaculty of Engineering, MTI University, Cairo, EgyptThis study investigates the q-fractional Ivancevic option pricing model using two advanced semi-analytical methods: the q-Laplace Residual Power Series Method (q-LRPSM) and the q-Homotopy Analysis Method (q-HAM). The q-LRPSM is introduced and adapted for the first time to solve q-fractional partial differential equations, offering accurate and efficient approximate solutions through a power series approach. The q-HAM builds on the traditional HAM by constructing a homotopy between an initial guess and the exact solution. Numerical simulations confirm the effectiveness and accuracy of both methods across various q-values and time steps, with 2D and 3D visualizations highlighting their rapid convergence. The study demonstrates that these methods provide a powerful framework for solving complex models in financial mathematics and applied sciences.http://www.sciencedirect.com/science/article/pii/S2090447925003867q-fractional calculusIvancevic option pricing modelSemi-analytical methodsHomotopy analysis methodLaplace residual power series method |
| spellingShingle | Khalid K. Ali Mohamed S. Mohamed M. Maneea Advanced semi-analytical techniques for the q-fractional Ivancevic option pricing model Ain Shams Engineering Journal q-fractional calculus Ivancevic option pricing model Semi-analytical methods Homotopy analysis method Laplace residual power series method |
| title | Advanced semi-analytical techniques for the q-fractional Ivancevic option pricing model |
| title_full | Advanced semi-analytical techniques for the q-fractional Ivancevic option pricing model |
| title_fullStr | Advanced semi-analytical techniques for the q-fractional Ivancevic option pricing model |
| title_full_unstemmed | Advanced semi-analytical techniques for the q-fractional Ivancevic option pricing model |
| title_short | Advanced semi-analytical techniques for the q-fractional Ivancevic option pricing model |
| title_sort | advanced semi analytical techniques for the q fractional ivancevic option pricing model |
| topic | q-fractional calculus Ivancevic option pricing model Semi-analytical methods Homotopy analysis method Laplace residual power series method |
| url | http://www.sciencedirect.com/science/article/pii/S2090447925003867 |
| work_keys_str_mv | AT khalidkali advancedsemianalyticaltechniquesfortheqfractionalivancevicoptionpricingmodel AT mohamedsmohamed advancedsemianalyticaltechniquesfortheqfractionalivancevicoptionpricingmodel AT mmaneea advancedsemianalyticaltechniquesfortheqfractionalivancevicoptionpricingmodel |